How to define or represent evil in logic
I think you're going to have to be reconciled to the subjective nature of reality.  Objectivity is only possible in very special cases such as a Q.E.D. in mathematics, or a solved gamed.  Rationality is bounded, and any intractable problem results in a state of subjectivity/indeterminacy.  Additionally, pure values do not carry moral implications, despite popular associations, although it would be possible to create a game where certain values have negative effects, and the harm they result in could be understood as evil.  (i.e. 666/616 has numerological associations, and numerology can be understood as a proto form of number theory.)


A simple way to define evil would be through behavioral models in Game Theory.
In Game Theory, there is a concept knowns as the superrational strategy. 
Superrationality may be understood as the logical/mathematical expression of the Golden Rule: "do unto others as you would have them do unto you."
The Golden Rule forms the basis for most religions, in the context of empathy/compassion and altruism.
If the agent is evil, it will always betray, even when the competitor has shown a willingness to cooperate.


Thus evil is defined as the opposite of the Golden Rule.  (Possibly we would call this the Brimstone Rule;)